Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×#10595529 |
| Fitting | C25×C32 ⋊ C22 |
| Sylow | C32 ⋊ C2×H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D32 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C23×D32 |
| Fitting | C25×C32 | C22 |
| socle | C23×C32 | C24 |
| hypercenter | C25 | D32 |
| hypocenter | C32 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C25 | |
3147 conjugacy classes of subgroups; only the 580 normal subgroups are shown.
This group has 3147 conjugacy classes of subgroups — too many to draw. Only its 580 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 144230);